2m-10+2m-12+1/2m+6=106

Solution for 2m-10+2m-12+1/2m+6=106 equation:

2m-10+2m-12+1/2m+6=106

We move all terms to the left:

2m-10+2m-12+1/2m+6-(106)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

4m+1/2m-122=0

We multiply all the terms by the denominator


4m*2m-122*2m+1=0

Wy multiply elements

8m^2-244m+1=0

a = 8; b = -244; c = +1;
Δ = b2-4ac
Δ = -2442-4·8·1
Δ = 59504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{59504}=\sqrt{16*3719}=\sqrt{16}*\sqrt{3719}=4\sqrt{3719}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-244)-4\sqrt{3719}}{2*8}=\frac{244-4\sqrt{3719}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-244)+4\sqrt{3719}}{2*8}=\frac{244+4\sqrt{3719}}{16}
$